Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport.

Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 microm in fibre diameter with approximately 60% porosity). A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis-Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant. Results show that within a few hours of culture process and for a perfusion velocity of the order of 10(-4) m s(-1), the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10(-3) Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 x 10(-5) m s(-1). But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant. Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.

Biomechanical aspects in tissue engineering.

This article provides a very brief overview of how some major mechanical properties of biological tissue and their substitutes can be described and quantified in basic form in order to understand their physiological functioning from the viewpoint of tissue regeneration, then allowing new developments in tissue engineering. After shortly reviewing the main rheological properties we have focused on the related phenomena of mass and momentum transport through tissue, considering the poroelastic characteristics of these media. Using very rough approach, it is shown how the biphasic nature of these media can influence mechanical stresses and nutriment feeding of the imbedded cells.

Cell mechanotransduction and interactions with biological tissues.

The biomechanical mechanisms involved in the processes of tissue remodeling and adaptation are reviewed with emphasis on mechanotransduction at the cellular level. New theoretical models associated with experimental rheological techniques are briefly commented.

Estimation of pressure gradients in pulsatile flow from magnetic resonance acceleration measurements.

A method for estimating pressure gradients from MR images is demonstrated. Making the usual assumption that the flowing medium is a Newtonian fluid, and with appropriate boundary conditions, the inertial forces (or acceleration components of the flow) are proportional to the pressure gradients. The technique shown here is based on an evaluation of the inertial forces from Fourier acceleration encoding. This method provides a direct measurement of the total acceleration defined as the sum of the velocity derivative vs. time and the convective acceleration. The technique was experimentally validated by comparing MR and manometer pressure gradient measurements obtained in a pulsatile flow phantom. The results indicate that the MR determination of pressure gradients from an acceleration measurement is feasible with a good correlation with the true measurements (r = 0.97). The feasibility of the method is demonstrated in the aorta of a normal volunteer. Magn Reson Med 44:66-72, 2000.

Stiffening response of a cellular tensegrity model.

Living cells exhibit, as most biological tissues, a stiffening (strain-hardening) response which reflects the nonlinearity of the stress-strain relationship. Tensegrity structures have been proposed as a comprehensive model of such a cell's mechanical response. Based on a theoretical model of a 30-element tensegrity structure, we propose a quantitative analysis of its nonlinear mechanical behavior under static conditions and large deformations. This study provides theoretical foundation to the passage from large-scale tensegrity models to microscale living cells, as well as the comparison between results obtained in biological specimens of different sizes. We found two non-dimensional parameters (L*-normalized element length and T*-normalized elastic tension) which govern the mechanical response of the structure for three types of loading tested (extension, compression and shear). The linear strain-hardening is uniquely observed for extension but differed for the two other types of loading tested. The stiffening response of the theoretical model was compared and discussed with the living cells stiffening response observed by different methods (shear flow experiments, micromanipulation and magnetocytometry).

Mechanical compression of small coronary vessels during the cardiac cycle.

Intramyocardial stresses appear to be an important factor in the degree of compression of the coronary vasculature, directly influencing the peripheral impedance of the coronary hemodynamic network. A method is presented for predicting variation in the luminal area of small vessels embedded in myocardial tissue, due to changes in surrounding stresses. Such stresses and strains were calculated as those generated in the wall of a cylindrical structure, a model of the cardiac ventricular wall. Based on the classical theory of linear elasticity and assumptions of superposition of strains generated within the medium by the cyclic variation of tissue pressure and fiber stress, changes in the inner cross-section area of microvessels were computed. Applied to coronary microvasculature, it was shown for the range of tested parameters that these microvessels are not likely to be subjected to instability phenomena and subsequent collapses, but rather show a small change in area. These results are in agreement with physiological observations concerning the degree of area reduction in arterioles and venules localized within the endocardial portion of the left ventricular wall. Based on this theory, analysis of variations in distensibility, compliance and resistance of microvessels, such as arterioles and venules, vs. internal pressure, and different cardiac states and locations within the myocardial wall is possible.

Non-invasive measurement of pulmonary arterial pressure: I. A haemodynamic modelling approach.

In order to monitor pulmonary arterial pressure (P) by any non-invasive imaging technique, a haemodynamic model of blood flow kinetics and wall mechanics has been developed. It is a one-dimensional model of pulsatile flow in an elastic pulmonary arterial trunk, assuming that blood is an incompressible fluid and viscous effects are negligible. The equations are P(t)-Pd = rho c2lnS(t)/Sd-1/2pw-2(t) Pd = (Sd/Ss)1/2Pp where, at any time of the ejection phase of systole, P(t), S(t) and w(t) are the pulmonary arterial pressure, cross-sectional area of the pulmonary artery and blood velocity averaged on the cross section S, respectively, PP is the pulse pressure, the difference between the peak systolic pressure and the diastolic pressure Pd; rho is blood density, c pulse wave velocity, and Ss and Sd are maximum (systolic) and minimum (diastolic) values of the cross-sectional area S. Using these equations, P(t) can be calculated if the three parameters, i.e. c, S(t) and w(t) are measured. So far, it has been impossible to measure the pulse wave velocity c non-invasively. We have investigated the calculation of c from S(t) and w(t) using the equation of continuity in the absence and presence of reflected pressure waves. The hypotheses of the haemodynamic model are discussed.

Non-invasive measurement of pulmonary arterial pressure: II. A radionuclide method.

Pulmonary artery pulse pressure (PP) and diastolic pressure (Pd) may be obtained by applying a haemodynamic model of blood flow kinetics and wall mechanics to the pulmonary artery: Pp = rho(ws/(Ss/Sd-1))2log(Ss/Sd)-1/2 rho w2s Pd = (Sd/Ss)1/2Pp where rho is blood density, ws is peak ejection velocity, and Ss and Sd are peak maximal and end diastolic cross-sectional areas of the main pulmonary artery. The different parameters of the equations were measured from radionuclide first pass and equilibrium studies. Radionuclide first pass studies were performed in 24 patients with intravenous injection of 20 mCi of 99Tcm red blood cells with a gamma camera in a 20 degrees right anterior oblique position: data were collected in list mode, i.e. a continuous sequence of spatial and temporal coordinates of each photon. Pulmonary arterial pressure was recorded simultaneously with a microtip catheter during the first pass study. Gated first pass images of the right side of the heart were reconstructed, regions of interest drawn over the right ventricle and the main pulmonary artery (MPA) and time-activity curves generated. Peak systolic (Cs) and end diastolic (Cd) counts obtained from the MPA curve were proportional to the cross sections Ss and Sd of the MPA and Ss/Sd = Cs/Cd. The diameter (D) of the pulmonary artery was calculated as the distance between the two zeros of the second derivative of a cross-sectional profile. The averaged cross-sectional area was S = pi D2/4. ECG gated blood pool studies were performed in a LAO 40 degrees position when the tracer was at equilibrium; they were processed automatically and the right ventricular end diastolic counts (EDC) converted into volume (EDV) using an aortic volume/count ratio. Right ventricular peak ejection rate (PER) was obtained from the RV time-activity curve and the instantaneous peak ejection velocity was calculated, ws = PER X EDV/S X EDC. PP and Pd were calculated in mmHg and the radionuclide method yielded pressure values that correlated reasonably with catheterisation values: PP(rad) = 0.99 PP(cath)-0.55, r = 0.84 and Pd(rad) = 0.67 Pd(cath) + 4.91, r = 0.74. We conclude that radionuclide techniques can provide a non-invasive method based on a haemodynamic model for measuring pulmonary arterial pressure.

Theoretical models in mechanics of the left ventricle.

Different rheological concepts and theoretical studies have been recently presented using models of myocardial mechanics. Complex analysis of the mechanical behavior of the left ventricular wall have been developed in order to estimate the local stresses and deformations that occur during the heart cycle as well as the ventricular stroke volume and pressure. Theoretical models have taken into account non-linear and viscoelastic passive properties of the myocardium tissue, when subjected to large deformations, through given strain energy functions or stress-strain relations. Different prolate spheroid geometries have been considered for such thick shell cardiac structure. During the active state of the contraction, the rheological behavior of the fibers has been described using different muscle models and relationships between fiber tension and strain, and activation degree. A forthcoming approach for bridging the gap between the knowledge of the muscle fiber microrheological properties and the study of the mechanical behavior of the entire ventricle, consists in including anisotropic and inhomogeneous effects through fiber direction field.

Harmonic and impulse rheological tests of biomaterials.

Up to now, not so much attention has been paid concerning the dynamic rheological behaviour of soft tissues although non linear viscoelastic effects have often been reported when mechanical properties of biomaterials are concerned. In order to characterize such properties different rheological tests have been proposed, the two principal being the study of the sample stresses responses to applied strains which are either harmonic with time or of step function type. Two different apparatus have been designed in our laboratory which allow specific rheological tests on biological materials under controlled environmental conditions. With one of them, harmonic uniaxial extension tests are performed in a large domain of frequencies (.001 Hz to 100 Hz) and forces (up to 20 daN); with the other, the samples are submitted to relaxation tests in uniaxial elongation up to 5 cm deformation within time duration of the order of 20 ms. The principal characteristics, limitations and performances of such apparatus are presented and few examples of data thus obtained are given. On the basis of quasi linear viscoelasticity models, it can be shown that both two types of tests with their proper limitations are leading to the same rheological parameters.

[Wall rheology and arterial hydrodynamics: theoretical and hydromechanical models (author's transl)]. / Rhéologie des parois et hydrodynamique artérielle. Modèles théoriques et hydromécaniques

Recent results in research on transport of macromolecules between blood and the arterial wall have shown that endothelial cells are very sensitive to mechanical events localised in the flow boundary layer. Cardiac pressure waves of finite amplitude are characterized by non linear propagation phenomena in which the fluid-wall interaction plays an important role through the wall rheology. Different models of the mechanical behavior of arterial wall have been studied and their influence on blood flow field have been analysed.